🧮 algebra

1. **State the problem:** Find the inverse function $g^{-1}(x)$ of the one-to-one function $g(x) = \frac{4x}{5x - 9}$ and determine the domain and range of $g^{-1}$. 2. **Find the

1. **State the problem:** Factor the linear expression $56w + 35x$. 2. **Recall the factoring rule:** To factor an expression, find the greatest common factor (GCF) of all terms an

1. **State the problem:** Factor the linear expression $20x - 90$. 2. **Recall the factoring rule:** To factor an expression, find the greatest common factor (GCF) of all terms and

1. **State the problem:** Evaluate the expression $$-12 \div (-3) - (-6)$$. 2. **Recall the order of operations:** Division and subtraction are performed from left to right.

1. **State the problem:** Evaluate the expression $5 + 4 \times (-9)$. 2. **Recall the order of operations:** Multiplication is performed before addition.

1. **State the problem:** We need to graph the system of equations and determine the solution for the system: $$6x - 3y = 3$$

1. **State the problem:** We are given two systems of equations and asked to graph them and choose the correct graph. The first system is:

1. **State the problem:** Find an expression equivalent to $\left(2x\right)^{-3}$. 2. **Recall the negative exponent rule:** For any nonzero number $a$, $a^{-n} = \frac{1}{a^n}$.

1. **Problem statement:** The product of two whole numbers is 72. We need to find the largest possible sum $A$ and the smallest possible sum $B$ of these two numbers, then calculat

1. **State the problem:** Solve for $x$ in the equation $$\frac{x}{20} = \sqrt{9\%}.$$\n\n2. **Understand the components:** The percentage $9\%$ means $\frac{9}{100} = 0.09$.\n\n3.

1. The problem asks to write an equation for the function graphed above, which is a parabola. 2. The general form of a parabola's equation is $$y = a(x - h)^2 + k$$ where $(h,k)$ i

1. **State the problem:** Simplify and evaluate the expression $$\frac{u^{\frac{2}{3} + 1}}{4^{\frac{5}{3}}} - \frac{4^{\frac{5}{3}}}{u^{\frac{2}{3} + 1}}$$. 2. **Rewrite exponents

1. The problem asks: How many zeros does the graphed polynomial function have? 2. Recall that zeros of a polynomial function are the x-values where the graph crosses or touches the

1. The problem asks for the number of zeros of the polynomial function $$y = (x - 8)(x + 3)^2$$. 2. The zeros of a polynomial are the values of $x$ that make $y=0$.

1. **State the problem:** We are given data points of engine speeds $x$ (in hundreds of RPMs) and corresponding average speeds $y$ (in miles per hour) of a pontoon boat. We want to

1. The problem asks to find a recursive formula for the sequence defined explicitly by $$a_n = 10(-4)^{n-1}$$ that depends on the previous term $$a_{n-1}$$. 2. Recall that a recurs

1. The problem is to understand the given 2x3 matrix: $$\begin{bmatrix} 12x^3 - 2 & 4 \\ 6x - 5 & 2 \end{bmatrix}$$

1. The problem states: "Twenty-nine is equal to the difference between two and one fourth of a number." We need to translate this sentence into an equation. 2. Let the number be re

1. **State the problem:** Michael has 1067.13 in his checking account. He plans to spend 510.71 on a television and the rest on speakers costing 46.00 each. We want to find the ine

1. **State the problem:** We need to graph the function $$y=\frac{7}{8}x^3$$ and plot five points: one at $$x=0$$, two with negative $$x$$ values, and two with positive $$x$$ value

1. **State the problem:** We are given the function $y = \frac{7}{8}x^3$ and want to understand its shape and behavior. 2. **Formula and rules:** This is a cubic function of the fo